Fig. 7
From: Topological phases of extended Su-Schrieffer-Heeger-Hubbard model
CP-AFQMC results of the extended interacting SSH model at the quarter-filling with \(J_{11}=J_{33}=0.1\) and \(U=10\) for (a)–(e). (a) Spin correlation \(\langle S_{z,j}S_{z,k}\rangle\) with \(\Delta _{J_3-J_1}=-0.7\), topological edge states occupying the \(1_{st}\) and \(N_{th}\) sites. (b) Spin correlation with \(\Delta _{J_3-J_1}=0.7\), topological edge states occupying the \(1_{st}\), \(3_{rd}\), \((N-2)_{th}\), and \(N_{th}\) sites. (c), (d) Spin correlation \(\langle S_{z,j}S_{z,k}\rangle\) above the critical magnetic field \(E_{B_c}\), with \(\Delta _{J_3-J_1}=-0.7\) in (c) and \(\Delta _{J_3-J_1}=0.7\) in (d). (e) The Rényi entropy with changing external magnetic field \(E_B\) and \(\Delta _{J_3-J_1}\). Each point has errorbars of \(E_B\) and S, and the dotted line is a schematic line connecting different \(\Delta _{J_3-J_1}\). (f) The critical field strength as a function of U and \(\Delta _{J_{3}-J_{1}}\), revealing that for a given \(\Delta _ {J _ 3 - J _ 1}\), the critical magnetic field decreases as U increases.
